NCERT Solutions for Class 8 Mathematics Chapter 11 – Mensuration
Classes 8, 9, and 10 Mathematics are significant for students as it forms the base for higher mathematical concepts, which will be introduced in Classes 11 and 12. Mathematics also plays an imperative role in most competitive examinations, especially for JEE aspirants.
Chapter 11 of Class 8 Mathematics is about Mensuration. In this chapter, students will learn about 2D shapes and 3D shapes, for example, triangles, rectangular, circles, quadrilaterals, cupids, cubes, cylinders, polygons, etc. They will do some measurements based on area, surface area, volume, and perimeter. The chapter will help them to learn about things that are directly connected to our real world.
Extramarks is the go-to online learning platform for Mathematics for lakhs of students. Our experienced Mathematics teachers have prepared NCERT Solutions and chapter notes after a lot of research and past question paper analysis. Students can refer to our NCERT Solutions for Class 8 Mathematics Chapter 11 to learn and practise all Mensuration concepts.
Along with the NCERT Solutions, students will find other study resources, including the CBSE syllabus, important questions with answer solutions, CBSE revision notes, etc. Extramarks provides comprehensive study materials for students to learn and prepare for their exams.
Key Topics Covered In NCERT Solutions for Class 8 Mathematics Chapter 11
Mensuration is a branch of geometry that deals with the measurement of length, area, and volume.
Our NCERT Solutions for Class 8 Mathematics Chapter 11 will cover topics related to Mensuration.
Introduction
In this chapter, the students will learn about closed 2-D, 3-D-shaped figures like triangles, rectangular, circles, quadrilaterals, cubes, cylinders, and polygons. This chapter will also teach how to calculate the perimeter, area, volume, and surface area.
Let us Recall
In the previous chapter, we studied the shapes and their measurements, for example,
| Shape |
Area |
| Rectangular |
L X B |
| Square |
L X L where L is the side of the square |
| Triangle |
½ x B x H |
| Parallelogram |
B x H |
| Circle |
π R^2 |
Area of Trapezium
To find out the area of the trapezium, we will divide the shape into two parts. First is the triangle part. The second is its rectangular part, and the third is its other triangle part. The sum of the area of both shapes is shown below.
Area of Trapezium =
Students will get more examples of calculating questions related to this topic in our NCERT Solutions for Class 8 Mathematics Chapter 11.
Area of a General Quadrilateral
Drawing one of a generic quadrilateral’s diagonals will allow us to divide it into two triangles. By “triangulating,” we can find a formula for any common quadrilateral.
Area of quadrilateral ABCD
= (area of ∆ ABC) + (area of ∆ ADC)
= ( 1/ 2 AC × h1 ) + ( 1/ 2 AC × h2 )
= 1 / 2 AC × ( h1 + h2 )
= 1 / 2 d ( h1 + h2 ) where d denotes the length of diagonal AC
Area of Polygon
Area of polygon can be calculated with the same method we use to calculate the area of the quadrilateral. Split the shapes into triangles and calculate the area quickly.
By constructing two diagonals AC and AD the pentagon ABCDE is divided into three parts. So, area ABCDE = area of ∆ ABC + area of ∆ ACD + area of ∆ AED.
Many students find it difficult to remember the formulas for calculating the area of different shapes. In our NCERT Solutions for Class 8 Mathematics Chapter 11 we have given multiple examples which have helped many students remember the formulas better. Students can register on Extramarks website and get full access to our study materials.
Solid Shapes
In earlier classes, the students had learned about 2D and 3D shapes. In this section, we will see some solid shapes such as cuboids, cubes, cylinders, etc.
Our Mathematics faculty members have provided excellent visual demonstrations to show different formats of solid shapes in our NCERT Solutions for Class 8 Mathematics Chapter 11. This helps students to better visualise each shape and remember it properly.
Surface area of Cube, Cuboid and Cylinder
It has six rectangular surfaces. To find out the surface area of a cuboid, do a sum of all the surfaces.
Write the dimension of each side. We know that a cuboid has three pairs of identical faces. To the total area of all the faces of the box we calculate the total surface area of a cuboid which is area I + area II + area III + area IV +area V + area VI
Surface area of a cuboid = h × l + b × l + b × h + l × h + b × h + l × b
So the total surface area = 2 (h × l + b × h + b × l) = 2(lb + bh + hl) where h, l and b are the height, length and width of the cuboid respectively.
Like a cuboid It has six rectangular surfaces. To find out the surface area of the cube, do a sum of all the surfaces.
The surface area of cube = Total Surface Area = 6(side)^2
It covers two parts of the cylinder. The first one is its top/bottom face, and the second one is its curved surface. To find out the cylinder’s surface area, we sum up both of the parts areas.
Surface Area of Cylinder = Curved Surface + Area of Circular top/base
or
Surface Area of Cylinder = 2πr (r + h)
Solved examples are given in our NCERT Solutions for Class 8 Mathematics Chapter 11. By practising these examples and related exercises, students will be able to infer different steps for calculating the surface areas of various shapes.
Volume of cube, cuboid and cylinder
It is a 3D figure. It has length, breadth, and height. To find out the volume of the cuboid, we will multiply all three dimensions.
The volume of Cuboid = L x B x H
The cube is a special type of a cuboid, where length, breadth and height are all equal.
Hence, volume of cube = L * L * L
It is also a 3d figure. We can determine the volume of any cylinder by multiplying its base area by its height.
The volume of the Cylinder = πr2 * h
Similar to the surface area examples, our NCERT Solutions for Class 8 Mathematics Chapter 11 also contains a lot of solved examples for calculating volume. These solutions also have a lot of topic-specific exercises which students can practise to become confident with the concepts.
Volume and capacity
- Volume is the amount of a solid that covers the space
- Capacity is the quantity of solid that a container can hold.
NCERT Solutions for Class 8 Mathematics Chapter 11: Exercise & Answer Solutions
Extramarks study materials contain a lot of self-practice exercises. These exercises cover different formats of questions from the NCERT Textbook and NCERT Exemplars.
All the questions will make concepts clearer for the students. The questions also cover the past years’ questions from the CBSE board exams. The step-by-step detailed workings given for each answer help students to revise the concepts and also get familiar with the various concepts covered in this chapter, Mensuration.
Click on the below links to view exercise-specific questions and solutions covered in our NCERT Class 8 Mathematics Chapter 11 Solutions:
Along with Class 8 Mathematics solutions, students can explore NCERT Solutions on our Extramarks website for all other primary and secondary classes.
Click on the links given below to gain access to the Extramarks exercises and solutions:
Extramarks platform has study solutions for all grades and subjects. Refer to the links below to get access to our NCERT Solutions study materials:
NCERT Exemplar Class 8 Mathematics Chapter 11
NCERT Exemplars are a golden resource that contains many exercises with different question formats. There are many questions to practice related to the chapter, and it covers all the essential topics and concepts of NCERT Class 8 Mathematics Chapter 11. The questions are NCERT-based advanced level questions. Once students become confident of solving questions from these books, they can quickly solve their NCERT textbook questions and hence will start scoring good marks in their examinations.
Students can perform well in CBSE Board and other competitive exams by referring to NCERT Exemplar and NCERT Solution.
Key Features of NCERT Solutions for Class 8 Mathematics Chapter 11
Extramarks study materials are widely trusted by all the stakeholders – students, parents, and teachers. The main reason for this trust is our high-quality research-oriented study materials that are prepared by experienced subject matter experts.
Some key features of our NCERT Solutions for Class 8 Mathematics Chapter 11.
- It covers all the concepts and topics of Mensuration.. So, students can confidently rely on our NCERT solutions for complete chapter revision.
- It also provides many questions to practice on all the topics and concepts.
- The solutions are built by taking the CBSE syllabus and strictly following the NCERT guidelines.
- We have given a lot of visual demonstrations about the shapes and their parameters for students to understand these concepts quickly and make learning fun for them.